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Paradoxes of probabilistic programming And How to Condition on Events of Measure Zero with Infinitesimal Probabilities

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2021年第POPL期5卷 1–26页

作者： Jacobs, Jules Radboud Univ Nijmegen Nijmegen Netherlands Delft Univ Technol Delft Netherlands

probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating likelihood at each observe statement, and using the likelihood to steer random choices and weigh results with inference algorithms such as importance sampling or MCMC. We argue that naive likelihood accumulation does not give desirable semantics and leads to paradoxes when an observe statement is used to condition on a measure-zero event, particularly when the observe statement is executed conditionally on random data. We show that the paradoxes disappear if we explicitly model measure-zero events as a limit of positive measure events, and that we can execute these type of probabilistic programs by accumulating infinitesimal probabilities rather than probability densities. Our extension improves probabilistic programming languages as an executable notation for probability distributions by making it more well-behaved and more expressive, by allowing the programmer to be explicit about which limit is intended when conditioning on an event of measure zero.

关键词： probabilistic programming

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JAX Based Parallel Inference for Reactive probabilistic programming 2022

JAX Based Parallel Inference for Reactive Probabilistic Prog...

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23rd International Conference on Languages, Compilers, and Tools for Embedded System (LCTES)

作者： Baudart, Guillaume Mandel, Louis Tekin, Reyyan PSL Univ DI ENS Ecole Normale Super CNRSInria Paris France IBM Res Armonk NY USA

ISBN: (纸本)9781450392662

ProbZelus is a synchronous probabilistic language for the design of reactive probabilistic models in interaction with an environment. Reactive inference methods continuously learn distributions over the unobserved parameters of the model from statistical observations. Unfortunately, this inference problem is in general intractable. Monte Carlo inference techniques thus rely on many independent executions to compute accurate approximations. These methods are expensive but can be parallelized. We propose to use JAX to parallelize ProbZelus reactive inference engine. JAX is a recent library to compile Python code which can then be executed on massively parallel architectures such as GPUs or TPUs. In this paper, we describe a new reactive inference engine implemented in JAX and the new associated JAX backend for ProbZelus. We show on existing benchmarks that our new parallel implementation outperforms the original sequential implementation for a high number of particles.

关键词： probabilistic programming Reactive programming Streaming Inference Parallel Computing Compilation

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Declarative probabilistic logic programming in discrete-continuous domains

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ARTIFICIAL INTELLIGENCE 2024年 337卷

作者： Dos Martires, Pedro Zuidberg De Raedt, Luc Kimmig, Angelika Orebro Univ Ctr Appl Autonomous Sensor Syst Orebro Sweden Katholieke Univ Leuven Dept Comp Sci Leuven Belgium Leuven AI Leuven Belgium

Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming languages owes much of its success to a declarative semantics, the so-called distribution semantics. However, the distribution semantics is limited to discrete random variables only. While PLP has been extended in various ways for supporting hybrid, that is, mixed discrete and continuous random variables, we are still lacking a declarative semantics for hybrid PLP that not only generalizes the distribution semantics and the modeling language but also the standard inference algorithm that is based on knowledge compilation. We contribute the measure semantics together with the hybrid PLP language DC-ProbLog (where DC stands for distributional clauses) and its inference engine infinitesimal algebraic likelihood weighting (IALW). These have the original distribution semantics, standard PLP languages such as ProbLog, and standard inference engines for PLP based on knowledge compilation as special cases. Thus, we generalize the state of the art of PLP towards hybrid PLP in three different aspects: semantics, language and inference. Furthermore, IALW is the first inference algorithm for hybrid probabilistic programming based on knowledge compilation.

关键词： probabilistic programming Declarative semantics Discrete-continuous distributions Likelihood weighting Logic programming Knowledge compilation Algebraic model counting

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SPPL: probabilistic programming with Fast Exact Symbolic Inference 2021

SPPL: Probabilistic Programming with Fast Exact Symbolic Inf...

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42nd ACM SIGPLAN International Conference on programming Language Design and Implementation (PLDI)

作者： Saad, Feras A. Rinard, Martin C. Mansinghka, Vikash K. MIT 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781450383912

We present the Sum-Product probabilistic Language (SPPL), a new probabilistic programming language that automatically delivers exact solutions to a broad range of probabilistic inference queries. SPPL translates probabilistic programs into sum-product expressions, a new symbolic representation and associated semantic domain that extends standard sum-product networks to support mixed-type distributions, numeric transformations, logical formulas, and pointwise and set-valued constraints. We formalize SPPL via a novel translation strategy from probabilistic programs to sum-product expressions and give sound exact algorithms for conditioning on and computing probabilities of events. SPPL imposes a collection of restrictions on probabilistic programs to ensure they can be translated into sum-product expressions, which allow the system to leverage new techniques for improving the scalability of translation and inference by automatically exploiting probabilistic structure. We implement a prototype of SPPL with a modular architecture and evaluate it on benchmarks the system targets, showing that it obtains up to 3500x speedups over state-of-the-art symbolic systems on tasks such as verifying the fairness of decision tree classifiers, smoothing hidden Markov models, conditioning transformed random variables, and computing rare event probabilities.

关键词： probabilistic programming symbolic execution

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Vate: Runtime Adaptable probabilistic programming for Java 1

Vate: Runtime Adaptable Probabilistic Programming for Java

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1st Workshop on Machine Learning and Systems (EuroMLSys)

作者： Goodman, Daniel Pocock, Adam Peck, Jason Steele, Guy Oracle Labs Redwood City CA 94065 USA

ISBN: (纸本)9781450382984

Inspired by earlier work on Augur, Vate is a probabilistic programming language for the construction of JVM based probabilistic models with an Object-Oriented interface. As a compiled language it is able to examine the dependency graph of the model to produce optimised code that can be dynamically targeted to different platforms. Using Gibbs Sampling, Metropolis-Hastings and variable marginalisation it can handle a range of model types and is able to efficiently infer values, estimate probabilities, and execute models.

关键词： probabilistic programming Java Augur MCMC Parallel programming

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Correctness of Sequential Monte Carlo Inference for probabilistic programming Languages 1

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30th European Symposium on programming (ESOP) Held as Part of the 24th European Joint Conferences on Theory and Practice of Software (ETAPS)

作者： Lunden, Daniel Borgstrom, Johannes Broman, David KTH Royal Inst Technol Digital Futures Stockholm Sweden KTH Royal Inst Technol EECS Stockholm Sweden Uppsala Univ Uppsala Sweden

ISBN: (数字)9783030720193

ISBN: (纸本)9783030720193;9783030720186

probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference algorithms, such as sequential Monte Carlo (SMC), Markov chain Monte Carlo (MCMC), or variational methods. Existing research on such algorithms mainly concerns their implementation and efficiency, rather than the correctness of the algorithms themselves when applied in the context of expressive PPLs. To remedy this, we give a correctness proof for SMC methods in the context of an expressive PPL calculus, representative of popular PPLs such as WebPPL, Anglican, and Birch. Previous work have studied correctness of MCMC using an operational semantics, and correctness of SMC and MCMC in a denotational setting without term recursion. However, for SMC inference-one of the most commonly used algorithms in PPLs as of today-no formal correctness proof exists in an operational setting. In particular, an open question is if the resample locations in a probabilistic program affects the correctness of SMC. We solve this fundamental problem, and make four novel contributions: (i) we extend an untyped PPL lambda calculus and operational semantics to include explicit resample terms, expressing synchronization points in SMC inference;(ii) we prove, for the first time, that subject to mild restrictions, any placement of the explicit resample terms is valid for a generic form of SMC inference;(iii) as a result of (ii), our calculus benefits from classic results from the SMC literature: a law of large numbers and an unbiased estimate of the model evidence;and (iv) we formalize the bootstrap particle filter for the calculus and discuss how our results can be further extended to other SMC algorithms.

关键词： probabilistic programming Sequential Monte Carlo Operational Semantics Functional programming Measure Theory

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Compiling Stan to Generative probabilistic Languages and Extension to Deep probabilistic programming 2021

Compiling Stan to Generative Probabilistic Languages and Ext...

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42nd ACM SIGPLAN International Conference on programming Language Design and Implementation (PLDI)

作者： Baudart, Guillaume Burroni, Javier Hirzel, Martin Mandel, Louis Shinnar, Avraham PSL Univ Ecole Normale Super INRIA Paris Paris France UMass Amherst Amherst MA USA IBM Res MIT IBM Watson AI Lab Armonk NY USA

ISBN: (纸本)9781450383912

Stan is a probabilistic programming language that is popular in the statistics community, with a high-level syntax for expressing probabilistic models. Stan differs by nature from generative probabilistic programming languages like Church, Anglican, or Pyro. This paper presents a comprehensive compilation scheme to compile any Stan model to a generative language and proves its correctness. We use our compilation scheme to build two new backends for the Stanc3 compiler targeting Pyro and NumPyro. Experimental results show that the NumPyro backend yields a 2.3x speedup compared to Stan in geometric mean over 26 benchmarks. Building on Pyro we extend Stan with support for explicit variational inference guides and deep probabilistic models. That way, users familiar with Stan get access to new features without having to learn a fundamentally new language.

关键词： probabilistic programming Semantics Stan Pyro

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Implementing a Library for probabilistic programming Using Non-strict Non-determinism

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THEORY AND PRACTICE OF LOGIC programming 2020年第1期20卷 147-175页

作者： Dylus, Sandra Christiansen, Jan Teegen, Finn Univ Kiel Kiel Germany Flensburg Univ Appl Sci Flensburg Germany

This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for probabilistic programming. In fact, the paradigms of functional logic and probabilistic programming are closely connected. That is, language characteristics from one area exist in the other and vice versa. For example, the concepts of non-deterministic choice and call-time choice as known from functional logic programming are related to and coincide with stochastic memoization and probabilistic choice in probabilistic programming, respectively. We will further see that an implementation based on the concepts of functional logic programming can have benefits with respect to performance compared to a standard list-based implementation and can even compete with full-blown probabilistic programming languages, which we illustrate by several benchmarks.

关键词： probabilistic programming functional logic programming non-determinism laziness call-time choice

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probabilistic programming: A review for environmental modellers

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ENVIRONMENTAL MODELLING & SOFTWARE 2019年 114卷 40-48页

作者： Krapu, Christopher Borsuk, Mark Duke Univ Dept Civil & Environm Engn 305 Teer Engn Bldg Box 90271 Durham NC 27706 USA Duke Univ Dept Stat Sci Durham NC 27706 USA

The development process for an environmental model involves multiple iterations of a planning-implementation-assessment cycle. probabilistic programming languages (PPLs) are designed to expedite this process with general-purpose methods for implementing models, efficiently inferring their parameters, and generating probabilistic predictions. probabilistic programming exists at the intersection of Bayesian statistics, machine learning, and process-based modelling and therefore can be of value to the environmental modelling community. In this review article, we explain how it can be used to accelerate model development and allow for statistical inference using more complicated models and larger data sets than previously possible. Specific challenges and limitations to employing such frameworks are also raised. We provide guidance to help modellers decide whether incorporating probabilistic programming in their work may improve the efficiency and quality of their analyses.

关键词： Bayesian statistics Parameter estimation Uncertainty quantification probabilistic programming

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probabilistic programming with Densities in SlicStan: Efficient, Flexible, and Deterministic

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2019年第POPL期3卷 1-30页

作者： Gorinova, Maria, I Gordon, Andrew D. Sutton, Charles Univ Edinburgh Edinburgh Midlothian Scotland Microsoft Res Cambridge Cambridge England Google Brain Mountain View CA USA

Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantics of the language has been mainly given in terms of intuition about implementation, and has not been formalised. This paper provides a formal treatment of the Stan language, and introduces the probabilistic programming language SlicStan - a compositional, self-optimising version of Stan. Our main contributions are (1) the formalisation of a core subset of Stan through an operational density-based semantics;(2) the design and semantics of the Stan-like language SlicStan, which facilities better code reuse and abstraction through its compositional syntax, more flexible functions, and information-flow type system;and (3) a formal, semantic-preserving procedure for translating SlicStan to Stan.

关键词： probabilistic programming information flow analysis

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